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Dissociation products and structures of solid H2S at strong compression

Yinwei Li,1 Lin Wang,2,3 Hanyu Liu,3,4 Yunwei Zhang,3 Jian Hao,1 Chris J. Pickard,5 Joseph R. Nelson,6 Richard J. Needs,6

Wentao Li,2 Yanwei Huang,2 Ion Errea,7,8 Matteo Calandra,9 Francesco Mauri,9 and Yanming Ma3,*

1School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, China2Center for High Pressure Science and Technology Advanced Research, Shanghai, 201203, China

3State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, China4Geophysical Laboratory, Carnegie Institution of Washington, Washington D.C. 20015, USA

5Department of Materials Science & Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom6Theory of Condensed Matter Group, Cavendish Laboratory, J J Thomson Avenue, Cambridge CB3 0HE, United Kingdom

7Donostia International Physics Center (DIPC), Manuel de Lardizabal pasealekua 4, 20018 Donostia-San Sebastian, Basque Country, Spain8Fisika Aplikatua 1 Saila, EUITI Bilbao, University of the Basque Country (UPV/EHU), Rafael Moreno

“Pitxitxi” Pasealekua 3, 48013 Bilbao, Basque Country, Spain9IMPMC, UMR CNRS 7590, Sorbonne Universites - UPMC Univ. Paris 06, MNHN, IRD, 4 Place Jussieu, F-75005 Paris, France

(Received 1 September 2015; revised manuscript received 18 November 2015; published 11 January 2016)

Hydrogen sulfides have recently received a great deal of interest due to the record high superconductingtemperatures of up to 203 K observed on strong compression of dihydrogen sulfide (H2S). A joint theoreticaland experimental study is presented in which decomposition products and structures of compressed H2S arecharacterized, and their superconducting properties are calculated. In addition to the experimentally knownH2S and H3S phases, our first-principles structure searches have identified several energetically competitivestoichiometries that have not been reported previously: H2S3, H3S2, HS2, and H4S3. In particular, H4S3 ispredicted to be thermodynamically stable within a large pressure range of 25–113 GPa. High-pressure x-raydiffraction measurements confirm the presence of H3S and H4S3 through decomposition of H2S that emerges at27 GPa and coexists with residual H2S, at least up to the highest pressure of 140 GPa studied in our experiments.Electron-phonon coupling calculations show that H4S3 has a small Tc of below 2 K, and that H2S is mainlyresponsible for the observed superconductivity of samples prepared at low temperature (<100 K).

DOI: 10.1103/PhysRevB.93.020103

Superconductivity with a transition temperature Tc of up to203 K was observed recently in solid H2S at megabar pressures,which is the highest record among all known superconductors[1]. Ashcroft suggested that metallic hydrogen would be asuperconductor at high pressures with a Tc around roomtemperature [2] and subsequently predicted that hydrogen-richmetallic compounds might also be superconducting at highpressures [3]. Early theoretical studies focused on high-pressure silicon and aluminum hydrides [4,5], and a numberof potential high-temperature superconductors have now beenproposed in compressed hydrogen-rich compounds, with Tcsestimated in the range of 40–250 K (e.g., GaH3 [6,7], SnH4

[8], GeH4 [9], NbH4 [10], Si2H6 [11], SiH4(H2)2 [12], CaH6

[13], YH3 [14], YH4 and YH6 [15]). Unfortunately, they havenot been realized in practice, in part because of demandingexperimental challenges. Very recent experimental studieshave observed superconductivity in compressed phosphine(PH3) with a Tc above 100 K [16].

The high pressure phase diagram of H2S has been studiedextensively. H2S is a sister molecule of H2O and is theonly known stable compound in the H-S system at ambientpressure. High-pressure diamond anvil cell experiments led tothe discovery of a metallic phase at about 96 GPa [17–28].However, partial decomposition of H2S and elemental sulfurwas observed in Raman [27] and XRD studies [22] atroom temperature above 27 GPa. H2S had not been con-sidered as a candidate for superconductivity because it was

*mym@jlu.edu.cn

believed to dissociate into elemental sulfur and hydrogenunder high pressures [29]. Recent first-principles structuresearches predicted energetically stable metallic structures ofH2S above 110 GPa [30] and excluded dissociation into itselements. An estimated maximum Tc for metallic H2S of80 K at 160 GPa was predicted [30]. Motivated by thisstudy, Drozdov et al. [1] performed high-pressure experimentson solid H2S looking for superconductivity and found anastonishing Tc of 203 K at 155 GPa [1]. Interestingly, H2Sshows complex superconducting behavior at high pressureswith the emergence of two different superconducting states.Samples prepared at low temperature (100 K) have a Tc of∼30 K at 110 GPa at the onset of superconductivity, whichincreases rapidly to a maximum value of 150 K at 200 GPa,while samples at room temperature or above show a maximumTc of 203 K at 155 GPa.

Strobel et al. synthesized another H-S compound, H3S, bycompressing a mixture of H2S and H2 above 3.5 GPa [31].The superconducting Tc of H3S at 200 GPa was recentlypredicted to be as high as 191–204 K [32], with H3S in acubic Im3m structure. The same Im3m structure was alreadypredicted to occur for H3O via the decomposition of water(H2O) at terapascal pressures [33]. The agreement betweenexperimental [1] and theoretical values of Tc [32] led tothe proposal by Drozdov et al. that H3S could be formedby decomposition of H2S and might be responsible for theobserved superconductivity at 203 K [1]. This proposal wassupported by first-principles density-functional-theory (DFT)studies which suggested that it is thermodynamically favorablefor H2S to decompose into H3S + S [34–36] at pressures

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above 43 GPa [35]. However, there is a lack of experimentalevidence to support the formation of H3S, and the low Tc

superconducting phase has not been fully explored. There isan urgent need to characterize the decomposition productsof compressed H2S in an effort to build an understanding ofthe complex superconducting behavior exhibited by the H-Ssystem.

Here we present a joint theoretical and experimental studyof compressed H2S which clarifies the possible decompositionproducts and their structures. First-principles DFT structuresearches were used to predict several stoichiometries (H2S3,H3S2, HS2, and H4S3) and a structure in H3S. High pressurex-ray diffraction (XRD) experiments demonstrate that above27 GPa, H2S partially decomposes into S + H3S + H4S3. H4S3

emerges as the major component at around 66 GPa and coexistswith a small fraction of H3S and residual H2S, at least up tothe highest pressure studied experimentally of 140 GPa.

Extensive structure searches over 44 H-S stoichiometriesat 25, 50, 100, and 150 GPa were performed using theCALYPSO [37,38] and AIRSS [4,39] methods, which have beensuccessfully used to investigate structures of materials at highpressures [4,13,40–46]. The underlying structural relaxationswere performed using the Vienna ab initio simulation package(VASP) [47] for CALYPSO and the CASTEP plane-wave code[48] for AIRSS. Electron-phonon coupling (EPC) calculationswere performed with density functional perturbation theoryusing the QUANTUM-ESPRESSO package [49]. XRD data werecollected at the 15U1 beamline at the Shanghai SynchrotronRadiation Facility (SSRF) with a monochromatic beam ofwavelength 0.6199 A. The diffraction patterns were integratedwith the FIT2D computer code [50] and fitted by Rietveldprofile matching using the GSAS+EXPGUI programs [51,52].More information about the calculations and experiments isprovided in the Supplemental Material [53].

Figure 1 shows convex hull diagrams at 25, 50, 100, and150 GPa which summarize the results of the structure searches.The effects of including quantum zero-point vibrational mo-tion are significant, and they tend to increase with pressure. Ourresults suggest that up to six H-S compounds lie on the convex

FIG. 1. Results from structure searching at 25 (a), 50 (b), 100(c), and 150 GPa (d). Convex hulls are shown as continuous lines,with (red) and without (black) the inclusion of zero point vibrationalenthalpy (ZPE).

hull at some pressures and are therefore thermodynamicallystable. Besides the experimentally known H2S and H3Scompounds, we predict four additional stable compounds:H4S3, H3S2, H2S3, and HS2. Note that H2S is predicted tobe stable only below 25 GPa, while H3S is predicted to appearat all pressures considered. Enthalpy calculations show thatH3S becomes energetically more stable than H2S + 1/2H2

at around 6 GPa (Supplemental Material, Fig. S1 [53]). Thepredicted H3S2 and H2S3 phases have very narrow pressureranges of stability and are unstable above 34 and 25 GPa,respectively (Supplemental Material, Fig. S3 [53]). We havetherefore omitted further discussion of these two compounds.HS2 is predicted to be energetically stable between 64 and 116GPa on the basis of static-lattice enthalpy calculations. Thestable pressure range was revised to be between 75 and 87GPa when the zero-point vibrational enthalpy was included(Supplemental Material, Fig. S9 [53]). The correspondingcrystallographic parameters and phonon dispersion curves areprovided in the Supplemental Material [53].

For H3S, besides the P1, Cccm, R3m, and Im3m structuresof earlier studies [32], our searches predict a monoclinic C2/cstructure (4 f.u/cell). The C2/c structure consists of weaklybonded H2S and H2 molecules (Supplemental Material, Fig.S1b [53]) and is calculated to be more stable at pressures of2–112 GPa than the Cccm structure proposed previously [32](Supplemental Material, Fig. S1a [53]). Static-lattice enthalpycalculations give a zero-temperature phase sequence for H3S ofP1 → C2/c (2 GPa) → R3m (112 GPa) → Im3m (180 GPa).

H4S3 adopts an orthorhombic P212121 (4 f.u./cell) structurethat consists of weakly bonded HS and H2S molecules at 25GPa [Fig. 2(a)]. The H-S bond lengths within the HS andH2S molecules are 1.354 A and 1.387–1.391 A, respectively,which are significantly shorter than the H-S separation of1.913–1.932 A between molecules. With increasing pressure,the neighboring molecules bond with each other forming

FIG. 2. Energetically favorable structures of H4S3 with spacegroups P212121 (a) and Pnma (b). Small and large spheres representH and S atoms, respectively. (c) Calculated enthalpy curves of theP212121 structure with respect to the Pnma structure for H4S3 as afunction of pressure. (d) Decomposition enthalpy curves of H4S3 into(H3S + S) as a function of pressure.

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FIG. 3. (a) XRD patterns of H2S collected at various pressuresat room temperature with an incident wavelength of 0.6199 A. (b)and (c) Rietveld refinements of XRD profiles at 45.6 GPa based onthe compositions Pc-H2S, I41/acd-S, C2/c-H3S, and P212121-H4S3

with phase fractions of 1147:85:31:1 and at 65.7 GPa based oncompositions of Pnma-H4S3, C2/c-H3S, and Pc-H2S with phasefractions of 5:3.4:1, respectively. The cross symbols and red solidlines represent observed and fitted patterns, respectively. The solidlines at the bottom are the difference between the observed andfitted patterns. Vertical bars under the pattern represent the calculatedpositions of reflections arising from the compositions.

planar H-S-H-S zigzag chains and puckered H-S-H-S chains,respectively. P212121 transforms to a Pnma structure at 60 GPa[Fig. 2(c)]. The convex hull data suggests two synthesis routesfor H4S3: (i) decomposition of 8H2S → S + 4H3S + H4S3

above 25 GPa; (ii) reaction of 4H3S + 5S → 3H4S3 in thepressure range of 25–113 GPa. Theoretically, it is found thatH4S3 decomposes into H3S + S above 113 GPa [Figs. 1(d)and 2(d)].

The H2S samples were initially compressed to 10 GPa atlow temperature (77 K) and then warmed to room temperature.Powder XRD patterns were then collected on increasingpressure from 10 to 140 GPa at room temperature, as shownin Fig. 3(a). The XRD patterns collected at pressures up to 46GPa are in excellent agreement with previous data [18–22], andthe successive transitions of phase I′ → phase IV → phase Vare well reproduced. The XRD data at 10 GPa correspond tophase I′. Phase IV with additional peaks at around 12◦ and 15◦[shown by arrows in Fig. 3(a)] was observed at 16 GPa. Thediffraction peaks of phase IV weaken at pressures above 27GPa, and a diffraction profile observed at 46 GPa is responsiblefor phase V. The XRD data show that the IV → V transitionbegins above 27 GPa, in excellent agreement with previousresults [19,22].

Previous high-pressure Raman [27] and XRD [22] studieshave claimed that decomposition of H2S occurs at roomtemperature above 27 GPa. Indeed, we found that H2S partiallydecomposes in phase V. Unfortunately, we have not foundit possible to resolve the decomposition products and theircrystal structures from our current XRD data. Therefore weuse the predicted structures and convex hull data to help inanalyzing the experimental data. At 50 GPa, our calculations

suggest an energetically allowed dissociation path of 8H2S →S + 4H3S + H4S3 [Fig. 1(b)]. The XRD profile at 46 GPa wastherefore fitted to a mixture of H2S + S + H3S + H4S3 byperforming Rietveld refinements using the most energeticallystable structures. Remarkably, we found that the XRD profilecan be well indexed by a mixture of Pc-structured H2S, I41/acd-structured S, C2/c-structured H3S, and P212121-structuredH4S3, with phase fractions (ratios of numbers of unit cells) of1147:85:31:1, as shown in Fig. 3(b). The existence of a largeproportion of H2S demonstrates the partial decomposition.We also attempted other Rietveld refinements fitting the XRDpatterns to pure H2S, H2S + S + H3S, or S + 4H3S + H4S3,but all of these fits gave poorer results (Supplemental Material,Fig. S11 [53]). The calculated decomposition pressure (30GPa) for 8H2S → S + 4H3S + H4S3 (Supplemental Material,Fig. S17 [53]) is in excellent agreement with the value of27 GPa observed in experiment [22].

With increasing pressure, more H2S decomposes, and itscontribution to the XRD signal is reduced. The XRD patterncollected at 66 GPa shows entirely different features to that at46 GPa. Rietveld refinement shows that a mixture of Pnma-structured H4S3, C2/c-structured H3S, and Pc-structured H2Swith phase fractions 5:3.4:1 gives the best fit to the experi-mental data [Fig. 3(c)]. The disappearance of elemental S andthe reduction in the ratio of H3S are understandable since areaction of 4H3S + 5S → 3H4S3 takes place as inferred fromour convex hull calculations [Figs. 1(b) and 1(c)]. The twoshoulders on the main peak at 15◦ originate primarily fromH3S and H2S. These shoulders weaken when the pressure isincreased to 82 GPa, and the XRD pattern can then be wellindexed by Pnma-structured H4S3, C2/c-structured H3S, andPmc21-structured H2S with a major contribution (86%) fromH4S3 [Fig. 4(a)]. We also tried to refine the XRD profile at82 GPa with the inclusion of HS2, which is calculated to bestable in between 75 and 87 GPa. However, the inclusion ofHS2 results in a poorer fit with higher Rp and Rwp values(Supplemental Material, Fig. S13(a) [53]), which excludesHS2 as a decomposition product. Our results demonstrate thatH4S3 coexists with H3S and H2S at least up to 140 GPa, thehighest pressure studied experimentally [Fig. 4(b)]. At thispressure, a refinement based on Pnma-structured H4S3 andC2/c-structured H3S leads to poorer fits with higher Rp andRwp values (Supplemental Material, Fig. S14 [53]), whichsupports the existence of residual H2S (about 1.6%).

FIG. 4. Rietveld refinements of XRD profiles at 81.3 GPa basedon Pnma-H4S3 + C2/c-H3S + Pmc21-H2S with phase fractions of43:6:1 (a) and at 139.5 GPa based on Pnma-H4S3 + R3m-H3S +P-1-H2S with phase fractions of 56:7:1 (c).

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FIG. 5. Superconducting transition temperatures (Tc) calculatedfor various H-S compounds and experimental values for compressedH2S [1]. Solid squares and circles show experimental data fromFig. 1(b) and Fig. 2(b) of Ref. [1], respectively, where different runsare represented by the same symbols. The open stars, squares, andcircles show calculated data from Ref. [30], Ref. [36], and Ref. [55],respectively. Open triangles denote calculated Tc for Pnma-H4S3

in the present study. Note that the Tc values (open squares) forIm3m-H3S taken from Ref. [36] include anharmonic effects, while allother estimated Tcs are calculated within the harmonic approximation.

H4S3 is predicted to become metallic at 102 GPa (Sup-plemental Material, Fig. S18 [53]). However, the calculatedelectron-phonon-coupling parameter (λ = 0.42) is very smallat 140 GPa due to the low density of states at the Fermi levelof 0.09 eV−1/atom. As a result, the Tc estimated from theAllen and Dynes modified McMillan equation [54] with μ∗ of0.16–0.13 is only 0.75–2.1 K at 140 GPa.

In Fig. 5, we compare the calculated Tc values for H4S3,H2S, and H3S to experimental data measured in compressedH2S [1], where Tc obtained for samples prepared at low andhigh temperatures are denoted by L-Tc and H-Tc, respectively.On one hand, the observed L-Tc [1] at pressures below 160 GPacan only be quantitatively reproduced by H2S, while the natureof the rapidly increasing L-Tc above 160 GPa remains unclearbecause the calculated Tc values of H3S, H4S3, and H2S aretoo high, too low, and tending to decrease, respectively. On theother hand, although the values of Tc for Im3m structured H3Scalculated within the harmonic approximation are much higherthan the observed H-Tc [55], the inclusion of anharmoniceffects reproduces the H-Tc data above 180 GPa quite well[36]. However, at low pressures around 150 GPa, Tc values [55]estimated for R3m-H3S within the harmonic approximationare ∼45 K lower than the observed H-Tc. Meanwhile, thepredicted Tc for R3m-H3S increases with pressure, in starkcontrast to the experimental observation of a decrease in H-Tc.Further study is required to understand the steep Tc increaseof L-Tc above 160 GPa and the high H-Tc at around 150 GPa.

We find that kinetics plays an important role in determiningthe experimentally observed H-S structures. Theory suggeststhat H2S and H4S3 decompose above 30 and 113 GPa[Supplemental Material Fig. S17 and Fig. 2(d)], respectively.However, H2S and H4S3 are observed to persist up to at least

140 GPa. Large kinetic barriers must therefore play a majorrole in suppressing decomposition at high pressures, as hasbeen found in other materials [56–59].

In summary, first-principles structure searching calcula-tions have been used to predict four stable H-S compoundswith stoichiometries H3S2, H2S3, HS2, and H4S3 and aC2/c structure of H3S, enriching the phase diagram of H-Ssystems at high pressures. The formation of H4S3 andH3S was confirmed by XRD experiments to occur throughdecomposition of compressed H2S above 27 GPa resultingin the products S + H3S + H4S3. H4S3 becomes a majorcomponent at around 66 GPa and is stable up to at least140 GPa, with a small fraction of H3S and residual H2S. Wehave also examined potential superconductivity of metallicH4S3 via explicit calculations of electron-phonon couplingparameters and the superconducting Tc. Our work suggeststhat kinetically protected H2S in samples prepared at lowtemperature is responsible for the observed superconductivitybelow 160 GPa.

Note. Recently, we became aware of an unpublishedexperimental study [60] by Einaga et al. supporting theformation of H3S upon dissociation of H2S, in agreement withour experimental results. However, their results suggested thatH3S is the major component with some unidentified phases.We attribute this discrepancy to the different experimentalprotocols used in the two experiments: In our experimentssamples were compressed at ambient temperature above10 GPa, whereas in Ref. [60] a temperature of 220 K wasused. The unidentified minor phase in the data of Einaga et al.might be attributed to the H4S3 compound predicted here. It ispossible that the use of different experimental protocols couldgive rise to similar dissociation products with different phasefractions, depending on the exact path followed.

Y.L. and J.H. acknowledge funding from the NationalNatural Science Foundation of China under Grant No.11204111 and No. 11404148, the Natural Science Foundationof Jiangsu province under Grant No. BK20130223, andthe PAPD of Jiangsu Higher Education Institutions. Y.Z.and Y.M. acknowledge funding from the National NaturalScience Foundation of China under Grant Nos. 11274136 and11534003, the 2012 Changjiang Scholars Program of China.R.J.N. acknowledges financial support from the Engineeringand Physical Sciences Research Council (EPSRC) of theU.K. [EP/J017639/1]. Calculations were performed on theCambridge High Performance Computing Service facilityand the HECToR and Archer facilities of the U.K.’s na-tional high-performance computing service (for which accesswas obtained via the UKCP consortium [EP/K013564/1]).J.R.N. acknowledges financial support from the CambridgeCommonwealth Trust. I.E. acknowledges financial supportfrom the Spanish Ministry of Economy and Competitiveness(FIS2013-48286-C2-2-P). M.C. acknowledges support fromthe Graphene Flagship and Agence nationale de la recherche(ANR), Grant No. ANR-13-IS10-0003-01. Work at Carnegiewas partially supported by EFree, an Energy Frontier ResearchCenter funded by the DOE, Office of Science, Basic EnergySciences under Award No. DE-SC-0001057 (salary support forH.L.). The infrastructure and facilities used at Carnegie weresupported by NNSA Grant No. DE-NA-0002006, CDAC.

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